Fractional Quantum Hall States of Clustered Composite Fermions

Abstract

The energy spectra and wavefunctions of up to 14 interacting quasielectrons (QE's) in the Laughlin nu=1/3 fractional quantum Hall (FQH) state are investigated using exact numerical diagonalization. It is shown that at sufficiently high density the QE's form pairs or larger clusters. This behavior, opposite to Laughlin correlations, invalidates the (sometimes invoked) reapplication of the composite fermion picture to the individual QE's. The series of finite-size incompressible ground states are identified at the QE filling factors nu_QE=1/2, 1/3, 2/3, corresponding to the electron fillings nu=3/8, 4/11, 5/13. The equivalent quasihole (QH) states occur at nu_QH=1/4, 1/5, 2/7, corresponding to nu=3/10, 4/13, 5/17. All these six novel FQH states were recently discovered experimentally. Detailed analysis indicates that QE or QH correlations in these states are different from those of well-known FQH electron states (e.g., Laughlin or Moore-Read states), leaving the origin of their incompressibility uncertain. Halperin's idea of Laughlin states of QP pairs is also explored, but is does not seem adequate.

14 pages, 9 figures; revision: 1 new figure, some new references, some new data, title change

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Cited by in corpus (53)

• Non-Abelian Anyons and Topological Quantum Computation
• Quantum Hall Physics - hierarchies and CFT techniques
• Experimental studies of the fractional quantum Hall effect in the first excited Landau level
• Quantum Hall system in Tao-Thouless limit
• Fractional Quantum Hall Effect at Landau Level Filling nu=4/11
• Phase Diagram of Fractional Quantum Hall Effect of Composite Fermions in Multi-Component Systems
• Enigmatic 4/11 State: A Prototype for Unconventional Fractional Quantum Hall Effect
• Observation of Incompressibility at $\nu =4/11$ and $\nu =5/13$
• Unconventional fractional quantum Hall states and Wigner crystallization in suspended Corbino graphene
• Fractional Quantum Hall Effect at $\nu =2+6/13$: The Parton Paradigm for the Second Landau Level
• Evidence of a fractional quantum Hall nematic phase in a microscopic model
• Landau level mixing in the nu=5/2 fractional quantum Hall state
• Possible Anti-Pfaffian Pairing of Composite Fermions in the Lowest Landau Level
• Tripartite Composite Fermion States
• Hierarchy wave functions--from conformal correlators to Tao-Thouless states
• A note contrasting two microscopic theories of the fractional quantum Hall effect
• Moving crystal phases of a quantum Wigner solid in an ultra-high-quality 2D electron system
• Even-Denominator Fractional Quantum Hall State at Filling Factor ν = 3/4
• Abelian parton state for the $\nu =4/11$ fractional quantum Hall effect
• Composite-fermion pairing at half and quarter filled lowest Landau level
• Spin phase diagram of the nu_e=4/11 composite fermion liquid
• Fractionally charged skyrmions in fractional quantum Hall effect
• Interacting composite fermions: Nature of the 4/5, 5/7, 6/7, and 6/17 fractional quantum Hall states
• The Hierarchy of Incompressible Fractional Quantum Hall States
• Transition from Free to Interacting Composite Fermions away from $\nu$=1/3
• Particle-hole symmetry for composite fermions: An emergent symmetry in the fractional quantum Hall effect
• Second Generation of Moore-Read Quasiholes in a Composite Fermion Liquid
• Parton wave function for the fractional quantum Hall effect at $\nu =6/17$
• Three-body correlations and finite-size effects in the Moore--Read states on a sphere
• Static and Dynamic Properties of Type-II Composite Fermion Wigner Crystals
• Nature of the anomalous $4/13$ fractional quantum Hall effect in graphene
• Pair-distribution functions of correlated composite fermions
• Incompressible States of the Interacting Composite Fermions in Negative Effective Magnetic Fields at $\nu =4/13$, 5/17, and 3/10
• Phase diagram of the Two-Component Fractional Quantum Hall Effect
• States of interacting composite fermions at Landau level fillig $\nu =2+3/8$
• Anomalously low magnetoroton energies of the unconventional fractional quantum Hall states of composite fermions
• Quarter- and half-filled quantum Hall states and their topological orders revealed by daughter states in bilayer graphene
• Integral and fractional Quantum Hall Ising ferromagnets
• Signatures of correlated defects in an ultra-clean Wigner crystal in the extreme quantum limit
• Unconventional Filling Factor 4/11: A Closed-Form Ground State Wave Function
• Hyperspherical theory of the quantum Hall effect: the role of exceptional degeneracy
• Energy Spectra for Fractional Quantum Hall States
• Study of partially polarized fractional quantum Hall states
• Strongly correlated states of trapped ultracold fermions in deformed Landau levels
• Bubble phase at $\nu =1/3$ for a spinless hollow-core interaction
• Few-body collective excitations beyond Kohn's theorem in quantum Hall systems
• Generalization of Laughlin's Theory for the Fractional Quantum Hall Effect
• Frequency Dependence of Diagonal Resistance in Fractional Quantum Hall Effect via Periodic Modulation of Magnetic Field
• Second Generation of Composite Fermions and the Self-Similarity of the Fractional Quantum Hall Effect
• Topological correlations and breaking of fermionic antisymmetry of electrons in FQHE
• Exploring Quantum Hall Physics at Ultra-Low Temperatures and at High Pressures
• Topological Protection in a Landau Flat Band at $\nu =7/11$, a Candidate Filling Factor for Unconventional Correlations
• Cascade of fractional quantum Hall states in 2D system